Single-point blow-up for parabolic systems with exponential nonlinearities and unequal diffusivities

We study positive blowing-up solutions of systems of the form: $$u_t=delta_1 Delta u+e^{pv},quad v_t= delta_2Delta v+e^{qu},$$ with $delta_1,delta_2>0$ and $p, q>0$. We prove single-point blow-up for large classes of radially decreasing solutions. This answers a question left open in a paper of Friedman and Giga~(1987), where the result was obtained only for the equidiffusive case $delta_1=delta_2$ and the proof depended crucially on this assumption.